The ruin time under the Sparre-Andersen dual model

Yang, Chen; Sendova, Kristina P.

doi:10.1016/j.insmatheco.2013.10.012

Cited by 18 publications

(13 citation statements)

References 6 publications

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“…First-passage problems and ruin time are also much studied; see e.g. Landriault and Sendova [26], Mazza and Rullière [31], Zhu and Yang [43], Yang and Sendova [42] and Dimitrova et al [18]. There exists here a close and important connection with queueing models; see e.g.…”

Section: Introductionmentioning

confidence: 88%

Duality in ruin problems for ordered risk models

Goffard

Lefèvre

2018

Insurance: Mathematics and Economics

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On one hand, an ordered dual risk model is considered where the profit arrivals are governed by an order statistic point process (OSPP). First, the ruin time distribution is obtained in terms of Abel-Gontcharov polynomials. Then, by duality, the ruin time distribution is deduced for an insurance model where the claim amounts correspond to the inter-arrival times in an OSPP. On the other hand, an ordered insurance model is considered with an OSPP as claim arrival process. Lefèvre and Picard [28] determined the finite-time ruin probability in terms of Appell polynomials. Duality is used to derive the ruin probability in a dual model where the profit sizes correspond to the inter-arrival times of an OSPP.MSC 2010: 60G55, 60G40, 12E10.

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Section: Introductionmentioning

confidence: 88%

Duality in ruin problems for ordered risk models

Goffard

Lefèvre

2018

Insurance: Mathematics and Economics

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“…For example, Yao et al (2011) consider the dividend payments and capital injections control problem in a dual risk model. Further contributions in this strand of literature include Albrecher et al (2008), Avanzi et al (2007), Bayraktar and Egami (2008), Dai et al (2010), Dong and Liu (2010), Wen (2011) and Yang and Sendova (2014).…”

Section: S(t)mentioning

confidence: 99%

On finite-time ruin probabilities in a generalized dual risk model with dependence

Dimitrova

Kaishev

Zhao

2015

European Journal of Operational Research

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Citation: Dimitrova, D. S., Kaishev, V. K. and Zhao, S. (2015). On finite-time ruin probabilities in a generalized dual risk model with dependence. European Journal of Operational Research, 242(1), pp. 134-148. doi: 10.1016Research, 242(1), pp. 134-148. doi: 10. /j.ejor.2014 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractIn this paper, we study the finite-time ruin probability in a reasonably generalized dual risk model, where we assume any non-negative non-decreasing cumulative operational cost function and arbitrary capital gains arrival process. Establishing an enlightening link between this dual risk model and its corresponding insurance risk model, explicit expressions for the finite-time survival probability in the dual risk model are obtained under various general assumptions for the distribution of the capital gains. In order to make the model more realistic and general, different dependence structures among capital gains and inter-arrival times and between both are also introduced and corresponding ruin probability expressions are also given. The concept of alarm time, as introduced in Das and Kratz (2012), is applied to the dual risk model within the context of risk capital allocation. Extensive numerical illustrations are provided.

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“…Shi and Landriault [11] utilize the multivariate version of Lagrange expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely, the combination of exponentials. Yang and Sendova [12] study the Sparre Andersen dual risk model in which the times between positive gains are independently and identically distributed and have a generalized Erlang(n) distribution.…”

Section: The Risk Modelmentioning

confidence: 99%

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

Huang

2014

Mathematical Problems in Engineering

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This paper constructs a Sparre Andersen risk model with a constant dividend barrier in which the claim interarrival distribution is a mixture of an exponential distribution and an Erlang(n) distribution. We derive the integro-differential equation satisfied by the Gerber-Shiu discounted penalty function of this risk model. Finally, we provide a numerical example. The Risk ModelConsider a Sparre Andersen risk model,where ≥ 0 represents the initial capital, is the insurer's rate of premium income per unit time, and { ( ), ≥ 0} is the claim number process representing the number of claims up to time . { , ≥ 1} is a sequence of i.i.d. random variables representing the individual claim amounts with distribution function ( ) and density function ( ) with mean . We assume that { ( ), ≥ 0} and { , ≥ 1} are independent. Let { , ≥ 1} be sequence i.i.d. random variables, which represent the claim interarrival times, and has a density function ( ),where ≥ 1 is a positive integer, ≥ 0, 1 , 2 ≥ 0, and 1 + 2 = 1. We further assume that [ ] > [ ] for all , which ensure that lim → ∞ ( ) = ∞ almost surely. Throughout the paper we use the convention that ∑ 0 =1 = 0. In recent years the Sparre Andersen model has been studied extensively. Ruin probabilities and many ruin related quantities such as the marginal and joint defective distributions of the time to ruin, the deficit at ruin, the surplus prior to ruin, and the claim size causing ruin have received considerable attention. Some related results can be found in Cai and Dickson [1], Sun and Yang [2], Gerber and Shiu [3], and Ko [4]. Li and Garrido [5] consider a compound renewal (Sparre Andersen) risk process in the presence of a constant dividend barrier in which the claim waiting times are generalized Erlang(n) distributed. The Sparre Andersen model with phase-type interclaim times has been studied by Ren [6]. Ng and Yang [7] study the ruin probability and the distribution of the severity of ruin in risk models with phasetype claims. Landriault and Willmot [8] study the Gerber-Shiu function in a Sparre Andersen model with general interclaim times. Yang and Zhang [9] study a Sparre Andersen model in which the interclaim times are generalized Erlang(n) distributed. They assume that the premium rate is a step function depending on the current surplus level. Landriault and Sendova [10] generalize the Sparre Andersen dual risk model with Erlang(n) interinnovation times by adding a budget-restriction strategy. Shi and Landriault [11] utilize the multivariate version of Lagrange expansion theorem to obtain a series expansion for the density of the time to ruin under a more general distribution assumption, namely, the combination of exponentials. Yang and Sendova [12] study the Sparre Andersen dual risk model in which the times

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The ruin time under the Sparre-Andersen dual model

Cited by 18 publications

References 6 publications

Duality in ruin problems for ordered risk models

Duality in ruin problems for ordered risk models

On finite-time ruin probabilities in a generalized dual risk model with dependence

The Gerber-Shiu Discounted Penalty Function of Sparre Andersen Risk Model with a Constant Dividend Barrier

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